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The SKIRT project
advanced radiative transfer for astrophysics
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The SKIRT project
advanced radiative transfer for astrophysics
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SKIRT includes a mechanism to record and output photon arrival time lags. This enables self-consistent calculation of both the spectral and timing properties of reprocessed emission in a 3D model, with some limitations as discussed below. This user guide topic provides an overview of this feature, organized in sections as follows:
Information on the geometry of certain astrophysical systems can be obtained by studying the relative arrival times of reprocessed photons in different wavelength regimes. The SKIRT time lag mechanism determines the response to an infinitely short pulse emitted by the model source(s) across the full spectral range. Most models intended for timing studies will include a single point source placed at the model origin. However, if a model includes multiple or spatially distributed sources, all sources are assumed to simultaneously emit a pulse, whether this is physically meaningful or not.
Photon arrival time lags are determined by tracking the distance travelled by each photon packet. The origin of the arrival time is defined as the time at which a photon packet emitted at the spatial origin arrives at the observer directly. The time lag will be positive for photon packets that take a detour, for example, through scattering interactions. The time lag will be negative for sources closer to the observer than the spatial origin.
SKIRT offers two time lag instruments. The LightCurveInstrument records the both spatially and spectrally integrated flux density for each time lag interval in a user-configured time grid, and outputs the resulting light curve. The SpectralTimeMapInstrument records the spatially integrated flux density per wavelength interval and per time lag interval, and outputs a FITS file containing a 2D spectral-time map.
Both the LightCurveInstrument and the SpectralTimeMapInstrument derive from DistantInstrument, which means that they are assumed to be sufficiently distant from the observed model to justify the use of parallel projection. They also share the properties for configuring the line of sight with DistantInstrument. Both timing instruments record spatially integrated fluxes, and offer an option to limit this integration to photons arriving inside a given circular aperture. The calibration of output fluxes proceeds as described elsewhere for distant instruments.
Importantly, the timing instruments require the user to configure a time grid for discretizing the recorded time lags. For this purpose, SKIRT offers the following TimeGrid subclasses:
If needed, the InstrumentTimeGridProbe outputs detailed information on the time grids configured for each timing instrument.
The SpectralTimeMapInstrument evidently requires a wavelength grid for discretizing the recorded fluxes on the spectral axis, in addition to the discretization along the time lag axis. While the LightCurveInstrument does not discretize the recorded fluxes along the spectral axis, it still requires a wavelength grid to determine its spectral response. Most often, the wavelength grid is used to simply limit the spectral range of the recorded photons, but it is also possible to specify an arbitrary response curve. See the LightCurveInstrument class documentation for more information.
The LightCurveInstrument output units are W/m2/s (wavelength flavor) or 1/s/cm2/s (energy flavor). The SpectralTimeMapInstrument output units are W/m2/micron/s (wavelength flavor) or 1/s/cm2/keV/s (energy flavor).
The key assumption is that the time lag associated with each photon is fully determined by its geometrical path length, implying that interaction processes can be treated as effectively instantaneous. This is an excellent approximation for many physical processes implemented in SKIRT. In particular, scattering is intrinsically instantaneous, and fluorescence occurs on timescales that are entirely negligible compared to the light-travel times relevant for the systems under study.
However, care must be taken when extending the approach to processes in which energy exchange is not local in time. A clear example is absorption and re-emission by dust grains. This process involves energy storage and re-emission over a finite timescale that depends on grain properties and local conditions. A similar caveat may apply to photoionised plasmas, where recombination emission and line emission processes can introduce additional timescales. In such cases, the present implementation would not capture the full time-delay behaviour, and a more general treatment including process-dependent delay times would be required. To help avoid these issues, the current time lag mechanism is disabled for simulation modes that include secondary emission, i.e. it requires an "extinction-only" mode.
On the other hand, the time lag mechanism is fully compatible with SKIRT's implementation of kinematics (Doppler shifts) and with its treatment of polarisation.
SKIRT assumes photon propagation in Euclidean space, neglecting general relativistic effects such as light bending and gravitational time dilation. This approximation is appropriate only for regions sufficiently far from compact objects, where spacetime curvature is weak.
Most of the acceleration techniques implemented in SKIRT are fully compatible with the time lag mechanism. A prominent exception is the (approximate) line core skipping technique used in Lyα radiative transfer to effectively bypass large numbers of resonant scattering events. This technique must to be turned off for Lyα timing studies.
Finally, the accuracy of the derived timing observables is limited by Monte Carlo noise and by the adopted temporal binning. Applications that require high precision in the time lag distribution or higher-order timing diagnostics may demand a substantial number of photon packets, particularly in optically thick or multi-scattering regimes.